Let me ask a question , given 2 points on the XY plane and given the 2 tangents at them, how to compute an arbitrary chosen smooth curve passing the 2 given points. For details, traveling along the curve in one direction, the curvature must satisfy (Condition A or Condition B) given

Condition A. the curvature does not increase ;
Condition B. the curvature does not decrease.

@J.M. No. Although I knew the name , cspline, I had no idea of that it was the one I looked for . Thank you very much.
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seven_swodniwFeb 16 '12 at 16:20

The special case of curvature changing linearly with length along the curve is called an Euler spiral. You might find some information about fitting Euler spirals to points in Raph Levien's PhD thesis.
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RahulJan 1 '13 at 9:03